Most people value Alpine for its privacy. Unlike other expensive zip codes where high taxes pay for a bevvy of municipal services, Alpine has a relatively low tax rate, thanks in part to the fact that it doesn't have a high school or mail delivery.

In fact, it has barely any commerce at all--the only restaurant is Kiku, a hibachi house on the outskirts of town.

That doesn't necessarily mean the borough's housing market is booming, however. There are currently 54 homes with Alpine addresses on the market, according to Trulia (just five cost less than $1 million). "For Sale" signs hang all over town, most with the phone number of the local Sotheby's Realty office. And last year, prices were down 23% year-over-year, according to Forbes.